Notes:

This is a verse in a situation of longing, and by 'gathering'
is meant the beloved's gathering, and by 'message' is meant the 'sought-for
message', and he has brought in the word 'thirsty' because of wordplay
with the word 'cup'. (203)

He says, the gathering is held regularly every day. Every
day you go on joking with the Others, you go on giving to the Others, with
your own hand, cups full of wine. We are thirsty-lipped for the sought-for
message; that is, we remain deprived. Not even by accident are we ever invited
to the gathering of coquetry. Longing drips from the words. (261)

The extremity of complaint, the limit of longing drips from
it. That is, we who are in every way worthy of it, would never even be invited.
'Like this'-- that is, so much indifference toward us would be established
as permissible, that not even false inquiries would be made. 'Might take the
kisses of the cup'-- from this there passes before our eyes the scene at the
time of wine-drinking, with the Rivals
in a state of delightedly drinking wine, and the longing of the deprived rakish
one [rind]. (357-58)

FWP:

The two lines contrast the situation of the true lover with
that of the Others, but how? The commentators' consensus is that he's not
invited to the beloved's gatherings at all: he just stays home and tortures
himself with visions of how much fun they're having. If we look carefully,
however, we see that there are a number of possibilities

=the Others are invited to her gatherings; we are not
=the Others attend her gatherings; we do not (even if we're invited)
=the Others drink wine; we do not
=the Others flirtatiously 'kiss' the wine-cups; we do not

We are, in short, much harder to please than the Others are;
they will settle for a nice evening of sociability and drinking, while we
are 'thirsty-lipped' not for wine or company or flirtation, but only for a
'message'. Of course, the verse doesn't tell us what the 'message' is about--
but then, it's not hard for us to come up with some ideas. For surely the message would be as thirst-delighting and as intoxicating as wine, it would be as kissable as the rim of a delectable wine-glass.

Moreover, the whole thing is presented in the subjunctive
mode, depicting something that 'would' or 'might' occur. This element
of uncertainty adds to the multivalence of the verse. Could all this be hypothetical?
If so, the lover may be planning his tactics for the future. Or else the first
line could be construed as 'Others may take...' or 'Let others take...', while
the second line would proposes the behavior that we ourselves would then adopt.